1. Field of the Invention
The present invention relates to a three-dimensional periodic structure exhibiting a photonic band gap, and a functional element, e.g., a filter, a light-emitting device, or an optical circuit, including the same.
2. Description of the Related Art
The concept that the transmission-reflection characteristics and the like of electromagnetic waves are controlled by a structure that is smaller than or equal to a wavelength of light has been previously proposed by Yablonovitch (Physical Review Letters, Vol. 58, pp. 2059, 1987). According to this document, the transmission-reflection characteristics and the like of electromagnetic waves can be controlled by periodically arranging structures smaller than or equal to the wavelength of light, and the transmission-reflection characteristics of light can be controlled by reducing the wavelength of the electromagnetic waves to an order of the wavelength of the light. Such a structure is known as a photonic crystal, and it is indicated that a reflecting mirror having a reflectance of 100% and exhibiting no optical loss can be realized at some wavelength range. The above-described concept that the reflectance of 100% can be achieved at some wavelength range is referred to as a photonic band gap in contradistinction to an energy gap of a known semiconductor. The photonic band gap can be realized relative to light incident from every direction by making the structure a fine three-dimensional periodic structure. Hereafter, this is referred to as a complete photonic band gap. When the complete photonic band gap can be realized, various applications can be performed, for example, spontaneous emission from a light-emitting device can be reduced. Therefore, unprecedented and new functional elements can be realized. Furthermore, there is a demand for a functional element having a structure suitable for realizing a complete photonic band gap in a wider wavelength range.
Some structures exhibiting the above-described photonic band gap have been proposed (e.g., U.S. Pat. No. 6,392,787, U.S. Pat. No. 6,134,043, and Applied Physics Letters, Vol. 84, No. 3, pp. 362, 2004). Examples of three-dimensional periodic structures capable of realizing a complete photonic band gap include a diamond opal structure, a woodpile structure, a helical structure, a specific three-dimensional periodic structure, a structure realized by inverting the above-described three-dimensional periodic structure (an inverse structure), and a diamond woodpile structure, shown in FIGS. 12A to 12F in that order.
In general, three-dimensional periodic structures exhibiting photonic band gaps have structures that are small and are not readily producible. Consequently, very few three-dimensional periodic structures are operated in light wave ranges (wavelength of a few micrometers or less in a vacuum).
Under such circumstances, the woodpile structure shown in FIG. 12B proposed in U.S. Pat. No. 5,335,240 is a structure which can be produced by stacking two-dimensional periodic structures. Therefore, among three-dimensional structures, the woodpile structure is the only one structure in which a photonic band gap has been experimentally observed. However, the woodpile structure has a small photonic band gap width as compared to an inverse opal structure which is believed to have the largest wavelength width of photonic band gap. Consequently, there is a problem in that realization of optical elements, e.g., waveguides and wavelength selection filters, which are operated in wide wavelength bands, are difficult. The diamond woodpile structure shown in FIG. 12F, proposed in Applied Physics Letters, Vol. 84, No. 3, pp. 362, 2004, is a structure in which square prisms are disposed between square columns, the square prism having a square bottom and a side length equal to the width of the square column. The diamond woodpile structure exhibits a photonic band gap slightly wider than that of the woodpile structure, although the difference therebetween is small. On the other hand, it is difficult to produce the inverse opal structure by a technique used for a known semiconductor production process.